I bit ago, I tweeted a question that suddenly occurred to me when I was watching an interview of Noel Fielding right after reading a little about Richard Feynman. Can art and maths be the same? Can we have not just mathematical art, but artistic maths, too? I did a bit of research and wrote this post as I went along this enlightening journey through the depths of artistic freedom and mathematical rigidity, unified into a blissful amalgamation of two highly interesting and perfectly juxtaposed fields.
Let’s start off with one of the most well known utilisations of mathematics in art; the golden ratio. The golden ratio is a value denoted by phi (φ) that’s roughly 1.618. The golden ratio is perhaps the most fascinating value that occurs throughout nature; perhaps more than pi. To quote author and astrophysicist Mario Livo,
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
I learned about the golden ratio roughly five years ago because it beautifully ties in with one of my favourite sequences by the aforementioned Leonardo of Pisa, otherwise known as Fibonacci. Yes, the Fibonacci sequence that many of you computer science students have been woefully practicing. The Fibonacci sequence is fascinating because it is found just about everywhere in nature. If there was a god, the golden ratio and the Fibonacci sequence would be in his blueprints and a hotkey on his calculator. The sequence is an addition of the previous two elements, starting from zero. It goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 and so on. The most interesting thing about this? Divide a Fibonacci number with its previous Fibonacci number, and you get the golden ratio (or a rough approximation). Divide 34 and 21 and you get 1.619 – the larger the numbers the closer you get. And this is artistically intriguing, even in nature.
Take a look at this sunflower for example; we see a pattern in those seeds down there in the middle. If you start from the centre and count seeds in an outward spiral, you will always find a Fibonacci number. This video will help explain it. That’s just one example. Let’s move on to the Fibonacci spiral, which is yet more beautiful and extravagant.
You’ll start to notice a pattern here already. The sides of each of these squares are progressively decreasing Fibonacci numbers. Divide their sides and you get the golden ratio. See how it all ties in? We find this spiral absolutely everwhere, from meager shells in the shallow sands of the sea, to hurricanes and the spiral arms of galaxies.
Well, that’s all in nature. Let’s get back to answering the first question – can we have artistic maths? But we haven’t even touched on mathematical art, if there is such a thing. Surely enough, thousands of years of human endeavor and our drive towards creating things like poetry, art and music have left us with many examples of those fields overlapping.
Salvador Dali used the golden ratio in his painting, The Sacrament of the Last Supper.
We have the amazing American band Tool, whose alternative metal themes are admittedly not for everyone, although they’re one of my favourites. Their song Lateralus is heavily influenced by the Fibonacci sequence in everything from their time signature to the number of syllables. Check it out. Tool’s fans are known to be the sort of people you wouldn’t want to meet in real life, but you have to admire the more mathematically influenced boundaries that they try to push, like The Holy Gift, an alternative playlist that again, is bound by Lord Fibonacci.
We found more of this in architecture, from the Parthenon to many mosques and churches around the world. One of the most famous architects is the renowned Buckminster Fuller, after which the Buckminster Fullerene, a sixty carbon atom molecule is named. Also called a ‘Bucky Ball’ – the Fullerene also coincides with the Fibonacci sequence along with much of intermolecular chemistry.
Apple supposedly utilises the golden ratio in their logos.
We find more intriguing mathematics in Penrose tiles. Da Vinci also supposedly used the golden ratio in everything from the Mona Lisa to the Vitruvian man, and hypothesised that the human body is anatomically linked to the golden ratio. Of course, we can’t forget Fractal art. Fractals are patterns where the smallest pattern repeats till you have a big pattern that is the same as the small one. My favourite type of fractal is a Mandelbrot set because it so quaintly links mathematics with art.
Now we’re getting somewhere. Mathematics is very interlinked with art, just as it is with everything else. Everything in the universe, every phenomenon – every star floating in the Milky Way, every tiny protozoan crawling about, every sneeze, every hug, every chemical reaction, can be explained with an equation. And that is what biologists and chemists and physicists and cosmologists and mathematicians strive towards; to explain the unknown. To have an answer to every question, and more.
Lastly, I’m going to show you something very cool. Here it is:
Written by Upamanyu Acharya